LMFDB - Embedded newform 221.2.m.a.205.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [221,2,Mod(69,221)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("221.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(221, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 221 = 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	221.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.76469388467$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	221.205
Dual form			221.2.m.a.69.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(1.50000 + 0.866025i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(3.00000 + 5.19615i) q^{10} +(3.00000 - 1.73205i) q^{11} +1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} -3.00000 q^{14} +(-3.00000 + 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(0.500000 - 0.866025i) q^{17} -3.46410i q^{18} +(-6.00000 - 3.46410i) q^{19} +(3.00000 + 1.73205i) q^{20} -1.73205i q^{21} +(3.00000 - 5.19615i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(-1.50000 + 0.866025i) q^{24} -7.00000 q^{25} +(-4.50000 - 4.33013i) q^{26} +5.00000 q^{27} +(-1.50000 + 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} +(-3.00000 + 5.19615i) q^{30} -1.73205i q^{31} +(4.50000 + 2.59808i) q^{32} +(3.00000 + 1.73205i) q^{33} -1.73205i q^{34} +(3.00000 - 5.19615i) q^{35} +(-1.00000 - 1.73205i) q^{36} +(6.00000 - 3.46410i) q^{37} -12.0000 q^{38} +(2.50000 - 2.59808i) q^{39} -6.00000 q^{40} +(-6.00000 + 3.46410i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(-4.00000 + 6.92820i) q^{43} -3.46410i q^{44} +(6.00000 + 3.46410i) q^{45} +(-4.50000 - 2.59808i) q^{46} +3.46410i q^{47} +(-2.50000 + 4.33013i) q^{48} +(-2.00000 - 3.46410i) q^{49} +(-10.5000 + 6.06218i) q^{50} +1.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} +9.00000 q^{53} +(7.50000 - 4.33013i) q^{54} +(6.00000 + 10.3923i) q^{55} +(1.50000 - 2.59808i) q^{56} -6.92820i q^{57} +(9.00000 + 5.19615i) q^{58} +(-12.0000 - 6.92820i) q^{59} +3.46410i q^{60} +(-2.00000 + 3.46410i) q^{61} +(-1.50000 - 2.59808i) q^{62} +(-3.00000 + 1.73205i) q^{63} -1.00000 q^{64} +(12.0000 - 3.46410i) q^{65} +6.00000 q^{66} +(-0.500000 - 0.866025i) q^{68} +(1.50000 - 2.59808i) q^{69} -10.3923i q^{70} +(3.00000 + 1.73205i) q^{71} +(3.00000 + 1.73205i) q^{72} +13.8564i q^{73} +(6.00000 - 10.3923i) q^{74} +(-3.50000 - 6.06218i) q^{75} +(-6.00000 + 3.46410i) q^{76} -6.00000 q^{77} +(1.50000 - 6.06218i) q^{78} +1.00000 q^{79} +(-15.0000 + 8.66025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} -10.3923i q^{83} +(-1.50000 - 0.866025i) q^{84} +(3.00000 + 1.73205i) q^{85} +13.8564i q^{86} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-13.5000 + 7.79423i) q^{89} +12.0000 q^{90} +(-1.50000 + 6.06218i) q^{91} -3.00000 q^{92} +(1.50000 - 0.866025i) q^{93} +(3.00000 + 5.19615i) q^{94} +(12.0000 - 20.7846i) q^{95} +5.19615i q^{96} +(-6.00000 - 3.46410i) q^{97} +(-6.00000 - 3.46410i) q^{98} -6.92820i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} - 3 q^{7} + 2 q^{9} + 6 q^{10} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 6 q^{14} - 6 q^{15} + 5 q^{16} + q^{17} - 12 q^{19} + 6 q^{20} + 6 q^{22} - 3 q^{23} - 3 q^{24}+ \cdots - 12 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 + q^3 + q^4 + 3 * q^6 - 3 * q^7 + 2 * q^9 + 6 * q^10 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 6 * q^14 - 6 * q^15 + 5 * q^16 + q^17 - 12 * q^19 + 6 * q^20 + 6 * q^22 - 3 * q^23 - 3 * q^24 - 14 * q^25 - 9 * q^26 + 10 * q^27 - 3 * q^28 + 6 * q^29 - 6 * q^30 + 9 * q^32 + 6 * q^33 + 6 * q^35 - 2 * q^36 + 12 * q^37 - 24 * q^38 + 5 * q^39 - 12 * q^40 - 12 * q^41 - 3 * q^42 - 8 * q^43 + 12 * q^45 - 9 * q^46 - 5 * q^48 - 4 * q^49 - 21 * q^50 + 2 * q^51 - 7 * q^52 + 18 * q^53 + 15 * q^54 + 12 * q^55 + 3 * q^56 + 18 * q^58 - 24 * q^59 - 4 * q^61 - 3 * q^62 - 6 * q^63 - 2 * q^64 + 24 * q^65 + 12 * q^66 - q^68 + 3 * q^69 + 6 * q^71 + 6 * q^72 + 12 * q^74 - 7 * q^75 - 12 * q^76 - 12 * q^77 + 3 * q^78 + 2 * q^79 - 30 * q^80 - q^81 - 12 * q^82 - 3 * q^84 + 6 * q^85 - 6 * q^87 + 6 * q^88 - 27 * q^89 + 24 * q^90 - 3 * q^91 - 6 * q^92 + 3 * q^93 + 6 * q^94 + 24 * q^95 - 12 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/221\mathbb{Z}\right)^\times$.

$n$	$105$	$171$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.135045	−	0.990839i	$-0.456882\pi$
$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.925615	+	0.378467i	$0.123549\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			3.46410i			1.54919i	0.632456	+	0.774597i	$0.282047\pi$
$5$			3.46410i			1.54919i	−0.632456	+	0.774597i	$0.717953\pi$
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	−1.50000	−	0.866025i	−0.566947	−	0.327327i	0.188982	−	0.981981i	$-0.439481\pi$
$7$	−1.50000	−	0.866025i	−0.566947	−	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$			1.73205i			0.612372i
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	3.00000	+	5.19615i	0.948683	+	1.64317i
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.0258656	−	0.999665i	$-0.491766\pi$
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.878668	+	0.477432i	$0.158432\pi$
$12$	1.00000			0.288675
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	−3.00000			−0.801784
$15$	−3.00000	+	1.73205i	−0.774597	+	0.447214i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$		−	3.46410i		−	0.816497i
$19$	−6.00000	−	3.46410i	−1.37649	−	0.794719i	−0.384759	−	0.923017i	$-0.625715\pi$
$19$	−6.00000	−	3.46410i	−1.37649	−	0.794719i	−0.991736	+	0.128298i	$0.959049\pi$
$20$	3.00000	+	1.73205i	0.670820	+	0.387298i
$21$		−	1.73205i		−	0.377964i
$22$	3.00000	−	5.19615i	0.639602	−	1.10782i
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	−7.00000			−1.40000
$26$	−4.50000	−	4.33013i	−0.882523	−	0.849208i
$27$	5.00000			0.962250
$28$	−1.50000	+	0.866025i	−0.283473	+	0.163663i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	4.50000	+	2.59808i	0.795495	+	0.459279i
$33$	3.00000	+	1.73205i	0.522233	+	0.301511i
$34$		−	1.73205i		−	0.297044i
$35$	3.00000	−	5.19615i	0.507093	−	0.878310i
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−12.0000			−1.94666
$39$	2.50000	−	2.59808i	0.400320	−	0.416025i
$40$	−6.00000			−0.948683
$41$	−6.00000	+	3.46410i	−0.937043	+	0.541002i	−0.889032	−	0.457845i	$-0.848621\pi$
$41$	−6.00000	+	3.46410i	−0.937043	+	0.541002i	−0.0480106	+	0.998847i	$0.515288\pi$
$42$	−1.50000	−	2.59808i	−0.231455	−	0.400892i
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		−	3.46410i		−	0.522233i
$45$	6.00000	+	3.46410i	0.894427	+	0.516398i
$46$	−4.50000	−	2.59808i	−0.663489	−	0.383065i
$47$			3.46410i			0.505291i	0.967559	+	0.252646i	$0.0813007\pi$
$47$			3.46410i			0.505291i	−0.967559	+	0.252646i	$0.918699\pi$
$48$	−2.50000	+	4.33013i	−0.360844	+	0.625000i
$49$	−2.00000	−	3.46410i	−0.285714	−	0.494872i
$50$	−10.5000	+	6.06218i	−1.48492	+	0.857321i
$51$	1.00000			0.140028
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$	7.50000	−	4.33013i	1.02062	−	0.589256i
$55$	6.00000	+	10.3923i	0.809040	+	1.40130i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		−	6.92820i		−	0.917663i
$58$	9.00000	+	5.19615i	1.18176	+	0.682288i
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.997027	−	0.0770484i	$-0.975450\pi$
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.565240	−	0.824927i	$-0.691216\pi$
$60$			3.46410i			0.447214i
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$	−1.50000	−	2.59808i	−0.190500	−	0.329956i
$63$	−3.00000	+	1.73205i	−0.377964	+	0.218218i
$64$	−1.00000			−0.125000
$65$	12.0000	−	3.46410i	1.48842	−	0.429669i
$66$	6.00000			0.738549
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		−	10.3923i		−	1.24212i
$71$	3.00000	+	1.73205i	0.356034	+	0.205557i	0.667340	−	0.744753i	$-0.267433\pi$
$71$	3.00000	+	1.73205i	0.356034	+	0.205557i	−0.311305	+	0.950310i	$0.600766\pi$
$72$	3.00000	+	1.73205i	0.353553	+	0.204124i
$73$			13.8564i			1.62177i	0.585206	+	0.810885i	$0.301014\pi$
$73$			13.8564i			1.62177i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	6.00000	−	10.3923i	0.697486	−	1.20808i
$75$	−3.50000	−	6.06218i	−0.404145	−	0.700000i
$76$	−6.00000	+	3.46410i	−0.688247	+	0.397360i
$77$	−6.00000			−0.683763
$78$	1.50000	−	6.06218i	0.169842	−	0.686406i
$79$	1.00000			0.112509			0.0562544	−	0.998416i	$-0.482084\pi$
$79$	1.00000			0.112509			0.0562544	+	0.998416i	$0.482084\pi$
$80$	−15.0000	+	8.66025i	−1.67705	+	0.968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$		−	10.3923i		−	1.14070i	−0.821401	−	0.570352i	$-0.806807\pi$
$83$		−	10.3923i		−	1.14070i	0.821401	−	0.570352i	$-0.193193\pi$
$84$	−1.50000	−	0.866025i	−0.163663	−	0.0944911i
$85$	3.00000	+	1.73205i	0.325396	+	0.187867i
$86$			13.8564i			1.49417i
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	−13.5000	+	7.79423i	−1.43100	+	0.826187i	−0.997197	−	0.0748225i	$-0.976161\pi$
$89$	−13.5000	+	7.79423i	−1.43100	+	0.826187i	−0.433800	+	0.901009i	$0.642828\pi$
$90$	12.0000			1.26491
$91$	−1.50000	+	6.06218i	−0.157243	+	0.635489i
$92$	−3.00000			−0.312772
$93$	1.50000	−	0.866025i	0.155543	−	0.0898027i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$	12.0000	−	20.7846i	1.23117	−	2.13246i
$96$			5.19615i			0.530330i
$97$	−6.00000	−	3.46410i	−0.609208	−	0.351726i	0.163448	−	0.986552i	$-0.447739\pi$
$97$	−6.00000	−	3.46410i	−0.609208	−	0.351726i	−0.772655	+	0.634826i	$0.781072\pi$
$98$	−6.00000	−	3.46410i	−0.606092	−	0.349927i
$99$		−	6.92820i		−	0.696311i
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	1.50000	−	0.866025i	0.148522	−	0.0857493i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	6.00000	−	1.73205i	0.588348	−	0.169842i
$105$	6.00000			0.585540
$106$	13.5000	−	7.79423i	1.31124	−	0.757042i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$			13.8564i			1.32720i	0.748086	+	0.663602i	$0.230973\pi$
$109$			13.8564i			1.32720i	−0.748086	+	0.663602i	$0.769027\pi$
$110$	18.0000	+	10.3923i	1.71623	+	0.990867i
$111$	6.00000	+	3.46410i	0.569495	+	0.328798i
$112$		−	8.66025i		−	0.818317i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$	−6.00000	−	10.3923i	−0.561951	−	0.973329i
$115$	9.00000	−	5.19615i	0.839254	−	0.484544i
$116$	6.00000			0.557086
$117$	−7.00000	−	1.73205i	−0.647150	−	0.160128i
$118$	−24.0000			−2.20938
$119$	−1.50000	+	0.866025i	−0.137505	+	0.0793884i
$120$	−3.00000	−	5.19615i	−0.273861	−	0.474342i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$			6.92820i			0.627250i
$123$	−6.00000	−	3.46410i	−0.541002	−	0.312348i
$124$	−1.50000	−	0.866025i	−0.134704	−	0.0777714i
$125$		−	6.92820i		−	0.619677i
$126$	−3.00000	+	5.19615i	−0.267261	+	0.462910i
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	0.906977	−	0.421180i	$-0.138384\pi$
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	−0.818241	+	0.574875i	$0.805051\pi$
$128$	−10.5000	+	6.06218i	−0.928078	+	0.535826i
$129$	−8.00000			−0.704361
$130$	15.0000	−	15.5885i	1.31559	−	1.36720i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$	3.00000	−	1.73205i	0.261116	−	0.150756i
$133$	6.00000	+	10.3923i	0.520266	+	0.901127i
$134$		0			0
$135$			17.3205i			1.49071i
$136$	1.50000	+	0.866025i	0.128624	+	0.0742611i
$137$	19.5000	+	11.2583i	1.66600	+	0.961864i	0.969763	+	0.244050i	$0.0784761\pi$
$137$	19.5000	+	11.2583i	1.66600	+	0.961864i	0.696235	+	0.717814i	$0.254857\pi$
$138$		−	5.19615i		−	0.442326i
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$	−3.00000	−	5.19615i	−0.253546	−	0.439155i
$141$	−3.00000	+	1.73205i	−0.252646	+	0.145865i
$142$	6.00000			0.503509
$143$	−9.00000	−	8.66025i	−0.752618	−	0.724207i
$144$	10.0000			0.833333
$145$	−18.0000	+	10.3923i	−1.49482	+	0.863034i
$146$	12.0000	+	20.7846i	0.993127	+	1.72015i
$147$	2.00000	−	3.46410i	0.164957	−	0.285714i
$148$		−	6.92820i		−	0.569495i
$149$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$149$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$150$	−10.5000	−	6.06218i	−0.857321	−	0.494975i
$151$			6.92820i			0.563809i	0.959442	+	0.281905i	$0.0909662\pi$
$151$			6.92820i			0.563809i	−0.959442	+	0.281905i	$0.909034\pi$
$152$	6.00000	−	10.3923i	0.486664	−	0.842927i
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$	−9.00000	+	5.19615i	−0.725241	+	0.418718i
$155$	6.00000			0.481932
$156$	−1.00000	−	3.46410i	−0.0800641	−	0.277350i
$157$	5.00000			0.399043			0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000			0.399043			0.199522	+	0.979893i	$0.436061\pi$
$158$	1.50000	−	0.866025i	0.119334	−	0.0688973i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$	−9.00000	+	15.5885i	−0.711512	+	1.23238i
$161$			5.19615i			0.409514i
$162$	−1.50000	−	0.866025i	−0.117851	−	0.0680414i
$163$	−9.00000	−	5.19615i	−0.704934	−	0.406994i	0.104248	−	0.994551i	$-0.466756\pi$
$163$	−9.00000	−	5.19615i	−0.704934	−	0.406994i	−0.809183	+	0.587557i	$0.800090\pi$
$164$			6.92820i			0.541002i
$165$	−6.00000	+	10.3923i	−0.467099	+	0.809040i
$166$	−9.00000	−	15.5885i	−0.698535	−	1.20990i
$167$	−7.50000	+	4.33013i	−0.580367	+	0.335075i	−0.761279	−	0.648424i	$-0.775428\pi$
$167$	−7.50000	+	4.33013i	−0.580367	+	0.335075i	0.180912	+	0.983499i	$0.442095\pi$
$168$	3.00000			0.231455
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	6.00000			0.460179
$171$	−12.0000	+	6.92820i	−0.917663	+	0.529813i
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$			10.3923i			0.787839i
$175$	10.5000	+	6.06218i	0.793725	+	0.458258i
$176$	15.0000	+	8.66025i	1.13067	+	0.652791i
$177$		−	13.8564i		−	1.04151i
$178$	−13.5000	+	23.3827i	−1.01187	+	1.75261i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$	6.00000	−	3.46410i	0.447214	−	0.258199i
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	3.00000	+	10.3923i	0.222375	+	0.770329i
$183$	−4.00000			−0.295689
$184$	4.50000	−	2.59808i	0.331744	−	0.191533i
$185$	12.0000	+	20.7846i	0.882258	+	1.52811i
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$		−	3.46410i		−	0.253320i
$188$	3.00000	+	1.73205i	0.218797	+	0.126323i
$189$	−7.50000	−	4.33013i	−0.545545	−	0.314970i
$190$		−	41.5692i		−	3.01575i
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−12.0000	+	6.92820i	−0.863779	+	0.498703i	−0.865276	−	0.501296i	$-0.832857\pi$
$193$	−12.0000	+	6.92820i	−0.863779	+	0.498703i	0.00149702	+	0.999999i	$0.499523\pi$
$194$	−12.0000			−0.861550
$195$	9.00000	+	8.66025i	0.644503	+	0.620174i
$196$	−4.00000			−0.285714
$197$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$197$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$198$	−6.00000	−	10.3923i	−0.426401	−	0.738549i
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		−	12.1244i		−	0.857321i
$201$		0			0
$202$	−9.00000	−	5.19615i	−0.633238	−	0.365600i
$203$		−	10.3923i		−	0.729397i
$204$	0.500000	−	0.866025i	0.0350070	−	0.0606339i
$205$	−12.0000	−	20.7846i	−0.838116	−	1.45166i
$206$	21.0000	−	12.1244i	1.46314	−	0.844744i
$207$	−6.00000			−0.417029
$208$	12.5000	−	12.9904i	0.866719	−	0.900721i
$209$	−24.0000			−1.66011
$210$	9.00000	−	5.19615i	0.621059	−	0.358569i
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$			3.46410i			0.237356i
$214$	−18.0000	−	10.3923i	−1.23045	−	0.710403i
$215$	−24.0000	−	13.8564i	−1.63679	−	0.944999i
$216$			8.66025i			0.589256i
$217$	−1.50000	+	2.59808i	−0.101827	+	0.176369i
$218$	12.0000	+	20.7846i	0.812743	+	1.40771i
$219$	−12.0000	+	6.92820i	−0.810885	+	0.468165i
$220$	12.0000			0.809040
$221$	−3.50000	−	0.866025i	−0.235435	−	0.0582552i
$222$	12.0000			0.805387
$223$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$223$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$224$	−4.50000	−	7.79423i	−0.300669	−	0.520774i
$225$	−7.00000	+	12.1244i	−0.466667	+	0.808290i
$226$		−	10.3923i		−	0.691286i
$227$	7.50000	+	4.33013i	0.497792	+	0.287401i	0.727801	−	0.685788i	$-0.240542\pi$
$227$	7.50000	+	4.33013i	0.497792	+	0.287401i	−0.230009	+	0.973189i	$0.573876\pi$
$228$	−6.00000	−	3.46410i	−0.397360	−	0.229416i
$229$		−	15.5885i		−	1.03011i	−0.857156	−	0.515057i	$-0.827771\pi$
$229$		−	15.5885i		−	1.03011i	0.857156	−	0.515057i	$-0.172229\pi$
$230$	9.00000	−	15.5885i	0.593442	−	1.02787i
$231$	−3.00000	−	5.19615i	−0.197386	−	0.341882i
$232$	−9.00000	+	5.19615i	−0.590879	+	0.341144i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$	−12.0000	+	3.46410i	−0.784465	+	0.226455i
$235$	−12.0000			−0.782794
$236$	−12.0000	+	6.92820i	−0.781133	+	0.450988i
$237$	0.500000	+	0.866025i	0.0324785	+	0.0562544i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$		−	24.2487i		−	1.56852i	−0.620433	−	0.784259i	$-0.713043\pi$
$239$		−	24.2487i		−	1.56852i	0.620433	−	0.784259i	$-0.286957\pi$
$240$	−15.0000	−	8.66025i	−0.968246	−	0.559017i
$241$	12.0000	+	6.92820i	0.772988	+	0.446285i	0.833939	−	0.551856i	$-0.186080\pi$
$241$	12.0000	+	6.92820i	0.772988	+	0.446285i	−0.0609515	+	0.998141i	$0.519414\pi$
$242$		−	1.73205i		−	0.111340i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	2.00000	+	3.46410i	0.128037	+	0.221766i
$245$	12.0000	−	6.92820i	0.766652	−	0.442627i
$246$	−12.0000			−0.765092
$247$	−6.00000	+	24.2487i	−0.381771	+	1.54291i
$248$	3.00000			0.190500
$249$	9.00000	−	5.19615i	0.570352	−	0.329293i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$			3.46410i			0.218218i
$253$	−9.00000	−	5.19615i	−0.565825	−	0.326679i
$254$	3.00000	+	1.73205i	0.188237	+	0.108679i
$255$			3.46410i			0.216930i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$	−12.0000	+	6.92820i	−0.747087	+	0.431331i
$259$	−12.0000			−0.745644
$260$	3.00000	−	12.1244i	0.186052	−	0.751921i
$261$	12.0000			0.742781
$262$	18.0000	−	10.3923i	1.11204	−	0.642039i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$			31.1769i			1.91518i
$266$	18.0000	+	10.3923i	1.10365	+	0.637193i
$267$	−13.5000	−	7.79423i	−0.826187	−	0.476999i
$268$		0			0
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$	15.0000	+	25.9808i	0.912871	+	1.58114i
$271$	−15.0000	+	8.66025i	−0.911185	+	0.526073i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−15.0000	+	8.66025i	−0.911185	+	0.526073i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	5.00000			0.303170
$273$	−6.00000	+	1.73205i	−0.363137	+	0.104828i
$274$	39.0000			2.35608
$275$	−21.0000	+	12.1244i	−1.26635	+	0.731126i
$276$	−1.50000	−	2.59808i	−0.0902894	−	0.156386i
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$		−	22.5167i		−	1.35046i
$279$	−3.00000	−	1.73205i	−0.179605	−	0.103695i
$280$	9.00000	+	5.19615i	0.537853	+	0.310530i
$281$			1.73205i			0.103325i	0.998665	+	0.0516627i	$0.0164521\pi$
$281$			1.73205i			0.103325i	−0.998665	+	0.0516627i	$0.983548\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$	3.00000	−	1.73205i	0.178017	−	0.102778i
$285$	24.0000			1.42164
$286$	−21.0000	−	5.19615i	−1.24176	−	0.307255i
$287$	12.0000			0.708338
$288$	9.00000	−	5.19615i	0.530330	−	0.306186i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−18.0000	+	31.1769i	−1.05700	+	1.83077i
$291$		−	6.92820i		−	0.406138i
$292$	12.0000	+	6.92820i	0.702247	+	0.405442i
$293$	13.5000	+	7.79423i	0.788678	+	0.455344i	0.839497	−	0.543364i	$-0.182850\pi$
$293$	13.5000	+	7.79423i	0.788678	+	0.455344i	−0.0508187	+	0.998708i	$0.516183\pi$
$294$		−	6.92820i		−	0.404061i
$295$	24.0000	−	41.5692i	1.39733	−	2.42025i
$296$	6.00000	+	10.3923i	0.348743	+	0.604040i
$297$	15.0000	−	8.66025i	0.870388	−	0.502519i
$298$		0			0
$299$	−7.50000	+	7.79423i	−0.433736	+	0.450752i
$300$	−7.00000			−0.404145
$301$	12.0000	−	6.92820i	0.691669	−	0.399335i
$302$	6.00000	+	10.3923i	0.345261	+	0.598010i
$303$	3.00000	−	5.19615i	0.172345	−	0.298511i
$304$		−	34.6410i		−	1.98680i
$305$	−12.0000	−	6.92820i	−0.687118	−	0.396708i
$306$	−3.00000	−	1.73205i	−0.171499	−	0.0990148i
$307$		−	3.46410i		−	0.197707i	−0.995102	−	0.0988534i	$-0.968483\pi$
$307$		−	3.46410i		−	0.197707i	0.995102	−	0.0988534i	$-0.0315175\pi$
$308$	−3.00000	+	5.19615i	−0.170941	+	0.296078i
$309$	7.00000	+	12.1244i	0.398216	+	0.689730i
$310$	9.00000	−	5.19615i	0.511166	−	0.295122i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$	4.50000	+	4.33013i	0.254762	+	0.245145i
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$	7.50000	−	4.33013i	0.423249	−	0.244363i
$315$	−6.00000	−	10.3923i	−0.338062	−	0.585540i
$316$	0.500000	−	0.866025i	0.0281272	−	0.0487177i
$317$			10.3923i			0.583690i	0.956466	+	0.291845i	$0.0942691\pi$
$317$			10.3923i			0.583690i	−0.956466	+	0.291845i	$0.905731\pi$
$318$	13.5000	+	7.79423i	0.757042	+	0.437079i
$319$	18.0000	+	10.3923i	1.00781	+	0.581857i
$320$		−	3.46410i		−	0.193649i
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$	4.50000	+	7.79423i	0.250775	+	0.434355i
$323$	−6.00000	+	3.46410i	−0.333849	+	0.192748i
$324$	−1.00000			−0.0555556
$325$	7.00000	+	24.2487i	0.388290	+	1.34508i
$326$	−18.0000			−0.996928
$327$	−12.0000	+	6.92820i	−0.663602	+	0.383131i
$328$	−6.00000	−	10.3923i	−0.331295	−	0.573819i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$			20.7846i			1.14416i
$331$	−9.00000	−	5.19615i	−0.494685	−	0.285606i	0.231831	−	0.972756i	$-0.425528\pi$
$331$	−9.00000	−	5.19615i	−0.494685	−	0.285606i	−0.726516	+	0.687150i	$0.758862\pi$
$332$	−9.00000	−	5.19615i	−0.493939	−	0.285176i
$333$		−	13.8564i		−	0.759326i
$334$	−7.50000	+	12.9904i	−0.410382	+	0.710802i
$335$		0			0
$336$	7.50000	−	4.33013i	0.409159	−	0.236228i
$337$	4.00000			0.217894			0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000			0.217894			0.108947	+	0.994048i	$0.465252\pi$
$338$	−10.5000	+	19.9186i	−0.571125	+	1.08343i
$339$	6.00000			0.325875
$340$	3.00000	−	1.73205i	0.162698	−	0.0939336i
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$	−12.0000	+	20.7846i	−0.648886	+	1.12390i
$343$			19.0526i			1.02874i
$344$	−12.0000	−	6.92820i	−0.646997	−	0.373544i
$345$	9.00000	+	5.19615i	0.484544	+	0.279751i
$346$		−	10.3923i		−	0.558694i
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	−0.340293	−	0.940319i	$-0.610526\pi$
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	0.984487	−	0.175457i	$-0.0561403\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	25.5000	−	14.7224i	1.36498	−	0.788074i	0.374701	−	0.927146i	$-0.377745\pi$
$349$	25.5000	−	14.7224i	1.36498	−	0.788074i	0.990282	+	0.139072i	$0.0444119\pi$
$350$	21.0000			1.12250
$351$	−5.00000	−	17.3205i	−0.266880	−	0.924500i
$352$	18.0000			0.959403
$353$	28.5000	−	16.4545i	1.51690	−	0.875784i	0.517099	−	0.855926i	$-0.327012\pi$
$353$	28.5000	−	16.4545i	1.51690	−	0.875784i	0.999803	−	0.0198582i	$-0.00632149\pi$
$354$	−12.0000	−	20.7846i	−0.637793	−	1.10469i
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$			15.5885i			0.826187i
$357$	−1.50000	−	0.866025i	−0.0793884	−	0.0458349i
$358$	9.00000	+	5.19615i	0.475665	+	0.274625i
$359$			3.46410i			0.182828i	0.995813	+	0.0914141i	$0.0291387\pi$
$359$			3.46410i			0.182828i	−0.995813	+	0.0914141i	$0.970861\pi$
$360$	−6.00000	+	10.3923i	−0.316228	+	0.547723i
$361$	14.5000	+	25.1147i	0.763158	+	1.32183i
$362$	12.0000	−	6.92820i	0.630706	−	0.364138i
$363$	1.00000			0.0524864
$364$	4.50000	+	4.33013i	0.235864	+	0.226960i
$365$	−48.0000			−2.51243
$366$	−6.00000	+	3.46410i	−0.313625	+	0.181071i
$367$	18.5000	+	32.0429i	0.965692	+	1.67263i	0.707744	+	0.706469i	$0.249713\pi$
$367$	18.5000	+	32.0429i	0.965692	+	1.67263i	0.257948	+	0.966159i	$0.416954\pi$
$368$	7.50000	−	12.9904i	0.390965	−	0.677170i
$369$			13.8564i			0.721336i
$370$	36.0000	+	20.7846i	1.87155	+	1.08054i
$371$	−13.5000	−	7.79423i	−0.700885	−	0.404656i
$372$		−	1.73205i		−	0.0898027i
$373$	11.5000	−	19.9186i	0.595447	−	1.03135i	−0.398036	−	0.917370i	$-0.630308\pi$
$373$	11.5000	−	19.9186i	0.595447	−	1.03135i	0.993484	−	0.113975i	$-0.0363585\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$	6.00000	−	3.46410i	0.309839	−	0.178885i
$376$	−6.00000			−0.309426
$377$	15.0000	−	15.5885i	0.772539	−	0.802846i
$378$	−15.0000			−0.771517
$379$	9.00000	−	5.19615i	0.462299	−	0.266908i	−0.250711	−	0.968062i	$-0.580665\pi$
$379$	9.00000	−	5.19615i	0.462299	−	0.266908i	0.713010	+	0.701153i	$0.247331\pi$
$380$	−12.0000	−	20.7846i	−0.615587	−	1.06623i
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$		−	10.3923i		−	0.531717i
$383$	12.0000	+	6.92820i	0.613171	+	0.354015i	0.774206	−	0.632934i	$-0.218150\pi$
$383$	12.0000	+	6.92820i	0.613171	+	0.354015i	−0.161034	+	0.986949i	$0.551483\pi$
$384$	−10.5000	−	6.06218i	−0.535826	−	0.309359i
$385$		−	20.7846i		−	1.05928i
$386$	−12.0000	+	20.7846i	−0.610784	+	1.05791i
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	−6.00000	+	3.46410i	−0.304604	+	0.175863i
$389$	−15.0000			−0.760530			−0.380265	−	0.924878i	$-0.624167\pi$
$389$	−15.0000			−0.760530			−0.380265	+	0.924878i	$0.624167\pi$
$390$	21.0000	+	5.19615i	1.06338	+	0.263117i
$391$	−3.00000			−0.151717
$392$	6.00000	−	3.46410i	0.303046	−	0.174964i
$393$	6.00000	+	10.3923i	0.302660	+	0.524222i
$394$		0			0
$395$			3.46410i			0.174298i
$396$	−6.00000	−	3.46410i	−0.301511	−	0.174078i
$397$	−21.0000	−	12.1244i	−1.05396	−	0.608504i	−0.130204	−	0.991487i	$-0.541563\pi$
$397$	−21.0000	−	12.1244i	−1.05396	−	0.608504i	−0.923755	+	0.382983i	$0.874897\pi$
$398$			27.7128i			1.38912i
$399$	−6.00000	+	10.3923i	−0.300376	+	0.520266i
$400$	−17.5000	−	30.3109i	−0.875000	−	1.51554i
$401$	21.0000	−	12.1244i	1.04869	−	0.605461i	0.126408	−	0.991978i	$-0.459655\pi$
$401$	21.0000	−	12.1244i	1.04869	−	0.605461i	0.922282	+	0.386517i	$0.126322\pi$
$402$		0			0
$403$	−6.00000	+	1.73205i	−0.298881	+	0.0862796i
$404$	−6.00000			−0.298511
$405$	3.00000	−	1.73205i	0.149071	−	0.0860663i
$406$	−9.00000	−	15.5885i	−0.446663	−	0.773642i
$407$	12.0000	−	20.7846i	0.594818	−	1.03025i
$408$			1.73205i			0.0857493i
$409$	−25.5000	−	14.7224i	−1.26089	−	0.727977i	−0.287646	−	0.957737i	$-0.592873\pi$
$409$	−25.5000	−	14.7224i	−1.26089	−	0.727977i	−0.973247	+	0.229759i	$0.926206\pi$
$410$	−36.0000	−	20.7846i	−1.77791	−	1.02648i
$411$			22.5167i			1.11066i
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$	12.0000	+	20.7846i	0.590481	+	1.02274i
$414$	−9.00000	+	5.19615i	−0.442326	+	0.255377i
$415$	36.0000			1.76717
$416$	4.50000	−	18.1865i	0.220631	−	0.891668i
$417$	13.0000			0.636613
$418$	−36.0000	+	20.7846i	−1.76082	+	1.01661i
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	0.999887	+	0.0150285i	$0.00478389\pi$
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	−0.486928	+	0.873442i	$0.661883\pi$
$420$	3.00000	−	5.19615i	0.146385	−	0.253546i
$421$		−	12.1244i		−	0.590905i	−0.955357	−	0.295452i	$-0.904530\pi$
$421$		−	12.1244i		−	0.590905i	0.955357	−	0.295452i	$-0.0954704\pi$
$422$	−19.5000	−	11.2583i	−0.949245	−	0.548047i
$423$	6.00000	+	3.46410i	0.291730	+	0.168430i
$424$			15.5885i			0.757042i
$425$	−3.50000	+	6.06218i	−0.169775	+	0.294059i
$426$	3.00000	+	5.19615i	0.145350	+	0.251754i
$427$	6.00000	−	3.46410i	0.290360	−	0.167640i
$428$	−12.0000			−0.580042
$429$	3.00000	−	12.1244i	0.144841	−	0.585369i
$430$	−48.0000			−2.31477
$431$	−16.5000	+	9.52628i	−0.794777	+	0.458865i	−0.841642	−	0.540037i	$-0.818410\pi$
$431$	−16.5000	+	9.52628i	−0.794777	+	0.458865i	0.0468646	+	0.998901i	$0.485077\pi$
$432$	12.5000	+	21.6506i	0.601407	+	1.04167i
$433$	14.5000	−	25.1147i	0.696826	−	1.20694i	−0.272736	−	0.962089i	$-0.587929\pi$
$433$	14.5000	−	25.1147i	0.696826	−	1.20694i	0.969561	−	0.244848i	$-0.0787382\pi$
$434$			5.19615i			0.249423i
$435$	−18.0000	−	10.3923i	−0.863034	−	0.498273i
$436$	12.0000	+	6.92820i	0.574696	+	0.331801i
$437$			20.7846i			0.994263i
$438$	−12.0000	+	20.7846i	−0.573382	+	0.993127i
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	−18.0000	+	10.3923i	−0.858116	+	0.495434i
$441$	−8.00000			−0.380952
$442$	−6.00000	+	1.73205i	−0.285391	+	0.0823853i
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$	6.00000	−	3.46410i	0.284747	−	0.164399i
$445$	−27.0000	−	46.7654i	−1.27992	−	2.21689i
$446$		0			0
$447$		0			0
$448$	1.50000	+	0.866025i	0.0708683	+	0.0409159i
$449$	−15.0000	−	8.66025i	−0.707894	−	0.408703i	0.102387	−	0.994745i	$-0.467352\pi$
$449$	−15.0000	−	8.66025i	−0.707894	−	0.408703i	−0.810281	+	0.586042i	$0.800685\pi$
$450$			24.2487i			1.14310i
$451$	−12.0000	+	20.7846i	−0.565058	+	0.978709i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	−6.00000	+	3.46410i	−0.281905	+	0.162758i
$454$	15.0000			0.703985
$455$	−21.0000	−	5.19615i	−0.984495	−	0.243599i
$456$	12.0000			0.561951
$457$	10.5000	−	6.06218i	0.491169	−	0.283577i	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	10.5000	−	6.06218i	0.491169	−	0.283577i	0.725059	+	0.688686i	$0.241812\pi$
$458$	−13.5000	−	23.3827i	−0.630814	−	1.09260i
$459$	2.50000	−	4.33013i	0.116690	−	0.202113i
$460$		−	10.3923i		−	0.484544i
$461$	−16.5000	−	9.52628i	−0.768482	−	0.443683i	0.0638511	−	0.997959i	$-0.479662\pi$
$461$	−16.5000	−	9.52628i	−0.768482	−	0.443683i	−0.832333	+	0.554276i	$0.812995\pi$
$462$	−9.00000	−	5.19615i	−0.418718	−	0.241747i
$463$		−	38.1051i		−	1.77090i	−0.464739	−	0.885448i	$-0.653852\pi$
$463$		−	38.1051i		−	1.77090i	0.464739	−	0.885448i	$-0.346148\pi$
$464$	−15.0000	+	25.9808i	−0.696358	+	1.20613i
$465$	3.00000	+	5.19615i	0.139122	+	0.240966i
$466$	9.00000	−	5.19615i	0.416917	−	0.240707i
$467$	30.0000			1.38823			0.694117	−	0.719862i	$-0.255795\pi$
$467$	30.0000			1.38823			0.694117	+	0.719862i	$0.255795\pi$
$468$	−5.00000	+	5.19615i	−0.231125	+	0.240192i
$469$		0			0
$470$	−18.0000	+	10.3923i	−0.830278	+	0.479361i
$471$	2.50000	+	4.33013i	0.115194	+	0.199522i
$472$	12.0000	−	20.7846i	0.552345	−	0.956689i
$473$			27.7128i			1.27424i
$474$	1.50000	+	0.866025i	0.0688973	+	0.0397779i
$475$	42.0000	+	24.2487i	1.92709	+	1.11261i
$476$			1.73205i			0.0793884i
$477$	9.00000	−	15.5885i	0.412082	−	0.713746i
$478$	−21.0000	−	36.3731i	−0.960518	−	1.66367i
$479$	−31.5000	+	18.1865i	−1.43927	+	0.830964i	−0.997799	−	0.0663107i	$-0.978877\pi$
$479$	−31.5000	+	18.1865i	−1.43927	+	0.830964i	−0.441473	+	0.897275i	$0.645544\pi$
$480$	−18.0000			−0.821584
$481$	−18.0000	−	17.3205i	−0.820729	−	0.789747i
$482$	24.0000			1.09317
$483$	−4.50000	+	2.59808i	−0.204757	+	0.118217i
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	12.0000	−	20.7846i	0.544892	−	0.943781i
$486$		−	27.7128i		−	1.25708i
$487$	4.50000	+	2.59808i	0.203914	+	0.117730i	0.598480	−	0.801138i	$-0.295772\pi$
$487$	4.50000	+	2.59808i	0.203914	+	0.117730i	−0.394566	+	0.918868i	$0.629105\pi$
$488$	−6.00000	−	3.46410i	−0.271607	−	0.156813i
$489$		−	10.3923i		−	0.469956i
$490$	12.0000	−	20.7846i	0.542105	−	0.938953i
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	−0.975898	−	0.218229i	$-0.929972\pi$
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	0.298957	−	0.954267i	$-0.403361\pi$
$492$	−6.00000	+	3.46410i	−0.270501	+	0.156174i
$493$	6.00000			0.270226
$494$	12.0000	+	41.5692i	0.539906	+	1.87029i
$495$	24.0000			1.07872
$496$	7.50000	−	4.33013i	0.336760	−	0.194428i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$	9.00000	−	15.5885i	0.403300	−	0.698535i
$499$			29.4449i			1.31813i	0.752085	+	0.659067i	$0.229048\pi$
$499$			29.4449i			1.31813i	−0.752085	+	0.659067i	$0.770952\pi$
$500$	−6.00000	−	3.46410i	−0.268328	−	0.154919i
$501$	−7.50000	−	4.33013i	−0.335075	−	0.193456i
$502$		0			0
$503$	16.5000	−	28.5788i	0.735699	−	1.27427i	−0.218718	−	0.975788i	$-0.570187\pi$
$503$	16.5000	−	28.5788i	0.735699	−	1.27427i	0.954416	−	0.298479i	$-0.0964794\pi$
$504$	−3.00000	−	5.19615i	−0.133631	−	0.231455i
$505$	18.0000	−	10.3923i	0.800989	−	0.462451i
$506$	−18.0000			−0.800198
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$	2.00000			0.0887357
$509$	10.5000	−	6.06218i	0.465404	−	0.268701i	−0.248910	−	0.968527i	$-0.580072\pi$
$509$	10.5000	−	6.06218i	0.465404	−	0.268701i	0.714314	+	0.699825i	$0.246739\pi$
$510$	3.00000	+	5.19615i	0.132842	+	0.230089i
$511$	12.0000	−	20.7846i	0.530849	−	0.919457i
$512$			8.66025i			0.382733i
$513$	−30.0000	−	17.3205i	−1.32453	−	0.764719i
$514$	9.00000	+	5.19615i	0.396973	+	0.229192i
$515$			48.4974i			2.13705i
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$	6.00000	+	10.3923i	0.263880	+	0.457053i
$518$	−18.0000	+	10.3923i	−0.790875	+	0.456612i
$519$	6.00000			0.263371
$520$	6.00000	+	20.7846i	0.263117	+	0.911465i
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$	18.0000	−	10.3923i	0.787839	−	0.454859i
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	−0.940129	+	0.340818i	$0.889296\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$			12.1244i			0.529150i
$526$	−18.0000	−	10.3923i	−0.784837	−	0.453126i
$527$	−1.50000	−	0.866025i	−0.0653410	−	0.0377247i
$528$			17.3205i			0.753778i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	27.0000	+	46.7654i	1.17281	+	2.03136i
$531$	−24.0000	+	13.8564i	−1.04151	+	0.601317i
$532$	12.0000			0.520266
$533$	18.0000	+	17.3205i	0.779667	+	0.750234i
$534$	−27.0000			−1.16840
$535$	36.0000	−	20.7846i	1.55642	−	0.898597i
$536$		0			0
$537$	−3.00000	+	5.19615i	−0.129460	+	0.224231i
$538$			41.5692i			1.79218i
$539$	−12.0000	−	6.92820i	−0.516877	−	0.298419i
$540$	15.0000	+	8.66025i	0.645497	+	0.372678i
$541$			6.92820i			0.297867i	0.988847	+	0.148933i	$0.0475840\pi$
$541$			6.92820i			0.297867i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	−15.0000	+	25.9808i	−0.644305	+	1.11597i
$543$	4.00000	+	6.92820i	0.171656	+	0.297318i
$544$	4.50000	−	2.59808i	0.192936	−	0.111392i
$545$	−48.0000			−2.05609
$546$	−7.50000	+	7.79423i	−0.320970	+	0.333562i
$547$	−7.00000			−0.299298			−0.149649	−	0.988739i	$-0.547814\pi$
$547$	−7.00000			−0.299298			−0.149649	+	0.988739i	$0.547814\pi$
$548$	19.5000	−	11.2583i	0.832999	−	0.480932i
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$	−21.0000	+	36.3731i	−0.895443	+	1.55095i
$551$		−	41.5692i		−	1.77091i
$552$	4.50000	+	2.59808i	0.191533	+	0.110581i
$553$	−1.50000	−	0.866025i	−0.0637865	−	0.0368271i
$554$			45.0333i			1.91328i
$555$	−12.0000	+	20.7846i	−0.509372	+	0.882258i
$556$	−6.50000	−	11.2583i	−0.275661	−	0.477460i
$557$	−7.50000	+	4.33013i	−0.317785	+	0.183473i	−0.650405	−	0.759588i	$-0.725401\pi$
$557$	−7.50000	+	4.33013i	−0.317785	+	0.183473i	0.332620	+	0.943061i	$0.392067\pi$
$558$	−6.00000			−0.254000
$559$	28.0000	+	6.92820i	1.18427	+	0.293032i
$560$	30.0000			1.26773
$561$	3.00000	−	1.73205i	0.126660	−	0.0731272i
$562$	1.50000	+	2.59808i	0.0632737	+	0.109593i
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	−0.711445	−	0.702742i	$-0.751959\pi$
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	0.964315	+	0.264758i	$0.0852922\pi$
$564$			3.46410i			0.145865i
$565$	18.0000	+	10.3923i	0.757266	+	0.437208i
$566$	−1.50000	−	0.866025i	−0.0630497	−	0.0364018i
$567$			1.73205i			0.0727393i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	−1.50000	−	2.59808i	−0.0628833	−	0.108917i	0.832870	−	0.553469i	$-0.186696\pi$
$569$	−1.50000	−	2.59808i	−0.0628833	−	0.108917i	−0.895753	+	0.444552i	$0.853363\pi$
$570$	36.0000	−	20.7846i	1.50787	−	0.870572i
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$	−12.0000	+	3.46410i	−0.501745	+	0.144841i
$573$	6.00000			0.250654
$574$	18.0000	−	10.3923i	0.751305	−	0.433766i
$575$	10.5000	+	18.1865i	0.437880	+	0.758431i
$576$	−1.00000	+	1.73205i	−0.0416667	+	0.0721688i
$577$			32.9090i			1.37002i	0.728535	+	0.685009i	$0.240202\pi$
$577$			32.9090i			1.37002i	−0.728535	+	0.685009i	$0.759798\pi$
$578$	−1.50000	−	0.866025i	−0.0623918	−	0.0360219i
$579$	−12.0000	−	6.92820i	−0.498703	−	0.287926i
$580$			20.7846i			0.863034i
$581$	−9.00000	+	15.5885i	−0.373383	+	0.646718i
$582$	−6.00000	−	10.3923i	−0.248708	−	0.430775i
$583$	27.0000	−	15.5885i	1.11823	−	0.645608i
$584$	−24.0000			−0.993127
$585$	6.00000	−	24.2487i	0.248069	−	1.00256i
$586$	27.0000			1.11536
$587$	−21.0000	+	12.1244i	−0.866763	+	0.500426i	−0.866271	−	0.499574i	$-0.833490\pi$
$587$	−21.0000	+	12.1244i	−0.866763	+	0.500426i	−0.000491641		1.00000i	$0.500156\pi$
$588$	−2.00000	−	3.46410i	−0.0824786	−	0.142857i
$589$	−6.00000	+	10.3923i	−0.247226	+	0.428207i
$590$		−	83.1384i		−	3.42276i
$591$		0			0
$592$	30.0000	+	17.3205i	1.23299	+	0.711868i
$593$		−	20.7846i		−	0.853522i	−0.904365	−	0.426761i	$-0.859655\pi$
$593$		−	20.7846i		−	0.853522i	0.904365	−	0.426761i	$-0.140345\pi$
$594$	15.0000	−	25.9808i	0.615457	−	1.06600i
$595$	−3.00000	−	5.19615i	−0.122988	−	0.213021i
$596$		0			0
$597$	−16.0000			−0.654836
$598$	−4.50000	+	18.1865i	−0.184019	+	0.743703i
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$	10.5000	−	6.06218i	0.428661	−	0.247487i
$601$	4.00000	+	6.92820i	0.163163	+	0.282607i	0.936002	−	0.351996i	$-0.114497\pi$
$601$	4.00000	+	6.92820i	0.163163	+	0.282607i	−0.772838	+	0.634603i	$0.781164\pi$
$602$	12.0000	−	20.7846i	0.489083	−	0.847117i
$603$		0			0
$604$	6.00000	+	3.46410i	0.244137	+	0.140952i
$605$	3.00000	+	1.73205i	0.121967	+	0.0704179i
$606$		−	10.3923i		−	0.422159i
$607$	−8.50000	+	14.7224i	−0.345004	+	0.597565i	−0.985355	−	0.170518i	$-0.945456\pi$
$607$	−8.50000	+	14.7224i	−0.345004	+	0.597565i	0.640350	+	0.768083i	$0.278789\pi$
$608$	−18.0000	−	31.1769i	−0.729996	−	1.26439i
$609$	9.00000	−	5.19615i	0.364698	−	0.210559i
$610$	−24.0000			−0.971732
$611$	12.0000	−	3.46410i	0.485468	−	0.140143i
$612$	−2.00000			−0.0808452
$613$	−18.0000	+	10.3923i	−0.727013	+	0.419741i	−0.817328	−	0.576172i	$-0.804546\pi$
$613$	−18.0000	+	10.3923i	−0.727013	+	0.419741i	0.0903153	+	0.995913i	$0.471213\pi$
$614$	−3.00000	−	5.19615i	−0.121070	−	0.209700i
$615$	12.0000	−	20.7846i	0.483887	−	0.838116i
$616$		−	10.3923i		−	0.418718i
$617$	12.0000	+	6.92820i	0.483102	+	0.278919i	0.721708	−	0.692197i	$-0.243357\pi$
$617$	12.0000	+	6.92820i	0.483102	+	0.278919i	−0.238606	+	0.971116i	$0.576691\pi$
$618$	21.0000	+	12.1244i	0.844744	+	0.487713i
$619$		−	5.19615i		−	0.208851i	−0.994533	−	0.104425i	$-0.966700\pi$
$619$		−	5.19615i		−	0.208851i	0.994533	−	0.104425i	$-0.0333004\pi$
$620$	3.00000	−	5.19615i	0.120483	−	0.208683i
$621$	−7.50000	−	12.9904i	−0.300965	−	0.521286i
$622$	18.0000	−	10.3923i	0.721734	−	0.416693i
$623$	27.0000			1.08173
$624$	17.5000	+	4.33013i	0.700561	+	0.173344i
$625$	−11.0000			−0.440000
$626$	15.0000	−	8.66025i	0.599521	−	0.346133i
$627$	−12.0000	−	20.7846i	−0.479234	−	0.830057i
$628$	2.50000	−	4.33013i	0.0997609	−	0.172791i
$629$		−	6.92820i		−	0.276246i
$630$	−18.0000	−	10.3923i	−0.717137	−	0.414039i
$631$	33.0000	+	19.0526i	1.31371	+	0.758470i	0.982708	−	0.185160i	$-0.0592804\pi$
$631$	33.0000	+	19.0526i	1.31371	+	0.758470i	0.331001	+	0.943630i	$0.392614\pi$
$632$			1.73205i			0.0688973i
$633$	6.50000	−	11.2583i	0.258352	−	0.447478i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−6.00000	+	3.46410i	−0.238103	+	0.137469i
$636$	9.00000			0.356873
$637$	−10.0000	+	10.3923i	−0.396214	+	0.411758i
$638$	36.0000			1.42525
$639$	6.00000	−	3.46410i	0.237356	−	0.137038i
$640$	−21.0000	−	36.3731i	−0.830098	−	1.43777i
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	−0.959848	−	0.280521i	$-0.909493\pi$
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	0.722862	+	0.690992i	$0.242826\pi$
$642$		−	20.7846i		−	0.820303i
$643$	19.5000	+	11.2583i	0.769005	+	0.443985i	0.832520	−	0.553996i	$-0.186898\pi$
$643$	19.5000	+	11.2583i	0.769005	+	0.443985i	−0.0635146	+	0.997981i	$0.520231\pi$
$644$	4.50000	+	2.59808i	0.177325	+	0.102379i
$645$		−	27.7128i		−	1.09119i
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	0.994270	+	0.106897i	$0.0340916\pi$
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	−0.404559	+	0.914512i	$0.632575\pi$
$648$	1.50000	−	0.866025i	0.0589256	−	0.0340207i
$649$	−48.0000			−1.88416
$650$	31.5000	+	30.3109i	1.23553	+	1.18889i
$651$	−3.00000			−0.117579
$652$	−9.00000	+	5.19615i	−0.352467	+	0.203497i
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$	−12.0000	+	20.7846i	−0.469237	+	0.812743i
$655$			41.5692i			1.62424i
$656$	−30.0000	−	17.3205i	−1.17130	−	0.676252i
$657$	24.0000	+	13.8564i	0.936329	+	0.540590i
$658$		−	10.3923i		−	0.405134i
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$	6.00000	+	10.3923i	0.233550	+	0.404520i
$661$	25.5000	−	14.7224i	0.991835	−	0.572636i	0.0860127	−	0.996294i	$-0.472587\pi$
$661$	25.5000	−	14.7224i	0.991835	−	0.572636i	0.905822	+	0.423658i	$0.139254\pi$
$662$	−18.0000			−0.699590
$663$	−1.00000	−	3.46410i	−0.0388368	−	0.134535i
$664$	18.0000			0.698535
$665$	−36.0000	+	20.7846i	−1.39602	+	0.805993i
$666$	−12.0000	−	20.7846i	−0.464991	−	0.805387i
$667$	9.00000	−	15.5885i	0.348481	−	0.603587i
$668$			8.66025i			0.335075i
$669$		0			0
$670$		0			0
$671$			13.8564i			0.534921i
$672$	4.50000	−	7.79423i	0.173591	−	0.300669i
$673$	−10.0000	−	17.3205i	−0.385472	−	0.667657i	0.606363	−	0.795188i	$-0.292628\pi$
$673$	−10.0000	−	17.3205i	−0.385472	−	0.667657i	−0.991835	+	0.127532i	$0.959295\pi$
$674$	6.00000	−	3.46410i	0.231111	−	0.133432i
$675$	−35.0000			−1.34715
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	−24.0000			−0.922395			−0.461197	−	0.887298i	$-0.652580\pi$
$677$	−24.0000			−0.922395			−0.461197	+	0.887298i	$0.652580\pi$
$678$	9.00000	−	5.19615i	0.345643	−	0.199557i
$679$	6.00000	+	10.3923i	0.230259	+	0.398820i
$680$	−3.00000	+	5.19615i	−0.115045	+	0.199263i
$681$			8.66025i			0.331862i
$682$	−9.00000	−	5.19615i	−0.344628	−	0.198971i
$683$	40.5000	+	23.3827i	1.54969	+	0.894714i	0.998165	+	0.0605550i	$0.0192870\pi$
$683$	40.5000	+	23.3827i	1.54969	+	0.894714i	0.551525	+	0.834159i	$0.314046\pi$
$684$			13.8564i			0.529813i
$685$	−39.0000	+	67.5500i	−1.49011	+	2.58095i
$686$	16.5000	+	28.5788i	0.629973	+	1.09115i
$687$	13.5000	−	7.79423i	0.515057	−	0.297368i
$688$	−40.0000			−1.52499
$689$	−9.00000	−	31.1769i	−0.342873	−	1.18775i
$690$	18.0000			0.685248
$691$	−31.5000	+	18.1865i	−1.19832	+	0.691848i	−0.960180	−	0.279383i	$-0.909870\pi$
$691$	−31.5000	+	18.1865i	−1.19832	+	0.691848i	−0.238137	+	0.971232i	$0.576537\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$	−6.00000	+	10.3923i	−0.227921	+	0.394771i
$694$		−	41.5692i		−	1.57795i
$695$	39.0000	+	22.5167i	1.47935	+	0.854106i
$696$	−9.00000	−	5.19615i	−0.341144	−	0.196960i
$697$			6.92820i			0.262424i
$698$	25.5000	−	44.1673i	0.965189	−	1.67176i
$699$	3.00000	+	5.19615i	0.113470	+	0.196537i
$700$	10.5000	−	6.06218i	0.396863	−	0.229129i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	−22.5000	−	21.6506i	−0.849208	−	0.817151i
$703$	−48.0000			−1.81035
$704$	−3.00000	+	1.73205i	−0.113067	+	0.0652791i
$705$	−6.00000	−	10.3923i	−0.225973	−	0.391397i
$706$	28.5000	−	49.3634i	1.07261	−	1.85782i
$707$			10.3923i			0.390843i
$708$	−12.0000	−	6.92820i	−0.450988	−	0.260378i
$709$	−12.0000	−	6.92820i	−0.450669	−	0.260194i	0.257443	−	0.966293i	$-0.417120\pi$
$709$	−12.0000	−	6.92820i	−0.450669	−	0.260194i	−0.708113	+	0.706099i	$0.750453\pi$
$710$			20.7846i			0.780033i
$711$	1.00000	−	1.73205i	0.0375029	−	0.0649570i
$712$	−13.5000	−	23.3827i	−0.505934	−	0.876303i
$713$	−4.50000	+	2.59808i	−0.168526	+	0.0972987i
$714$	−3.00000			−0.112272
$715$	30.0000	−	31.1769i	1.12194	−	1.16595i
$716$	6.00000			0.224231
$717$	21.0000	−	12.1244i	0.784259	−	0.452792i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	−0.550700	−	0.834703i	$-0.685639\pi$
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	0.998224	+	0.0595683i	$0.0189724\pi$
$720$			34.6410i			1.29099i
$721$	−21.0000	−	12.1244i	−0.782081	−	0.451535i
$722$	43.5000	+	25.1147i	1.61890	+	0.934674i
$723$			13.8564i			0.515325i
$724$	4.00000	−	6.92820i	0.148659	−	0.257485i
$725$	−21.0000	−	36.3731i	−0.779920	−	1.35086i
$726$	1.50000	−	0.866025i	0.0556702	−	0.0321412i
$727$	−26.0000			−0.964287			−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000			−0.964287			−0.482143	+	0.876092i	$0.660142\pi$
$728$	−10.5000	−	2.59808i	−0.389156	−	0.0962911i
$729$	13.0000			0.481481
$730$	−72.0000	+	41.5692i	−2.66484	+	1.53855i
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$	−2.00000	+	3.46410i	−0.0739221	+	0.128037i
$733$			1.73205i			0.0639748i	0.999488	+	0.0319874i	$0.0101836\pi$
$733$			1.73205i			0.0639748i	−0.999488	+	0.0319874i	$0.989816\pi$
$734$	55.5000	+	32.0429i	2.04854	+	1.18273i
$735$	12.0000	+	6.92820i	0.442627	+	0.255551i
$736$		−	15.5885i		−	0.574598i
$737$		0			0
$738$	12.0000	+	20.7846i	0.441726	+	0.765092i
$739$	30.0000	−	17.3205i	1.10357	−	0.637145i	0.166412	−	0.986056i	$-0.446782\pi$
$739$	30.0000	−	17.3205i	1.10357	−	0.637145i	0.937156	+	0.348911i	$0.113448\pi$
$740$	24.0000			0.882258
$741$	−24.0000	+	6.92820i	−0.881662	+	0.254514i
$742$	−27.0000			−0.991201
$743$	39.0000	−	22.5167i	1.43077	−	0.826056i	0.433592	−	0.901109i	$-0.357246\pi$
$743$	39.0000	−	22.5167i	1.43077	−	0.826056i	0.997180	+	0.0750533i	$0.0239127\pi$
$744$	1.50000	+	2.59808i	0.0549927	+	0.0952501i
$745$		0			0
$746$		−	39.8372i		−	1.45854i
$747$	−18.0000	−	10.3923i	−0.658586	−	0.380235i
$748$	−3.00000	−	1.73205i	−0.109691	−	0.0633300i
$749$			20.7846i			0.759453i
$750$	6.00000	−	10.3923i	0.219089	−	0.379473i
$751$	−11.5000	−	19.9186i	−0.419641	−	0.726839i	0.576262	−	0.817265i	$-0.304511\pi$
$751$	−11.5000	−	19.9186i	−0.419641	−	0.726839i	−0.995903	+	0.0904254i	$0.971177\pi$
$752$	−15.0000	+	8.66025i	−0.546994	+	0.315807i
$753$		0			0
$754$	9.00000	−	36.3731i	0.327761	−	1.32463i
$755$	−24.0000			−0.873449
$756$	−7.50000	+	4.33013i	−0.272772	+	0.157485i
$757$	11.5000	+	19.9186i	0.417975	+	0.723953i	0.995736	−	0.0922527i	$-0.0294068\pi$
$757$	11.5000	+	19.9186i	0.417975	+	0.723953i	−0.577761	+	0.816206i	$0.696073\pi$
$758$	9.00000	−	15.5885i	0.326895	−	0.566198i
$759$		−	10.3923i		−	0.377217i
$760$	36.0000	+	20.7846i	1.30586	+	0.753937i
$761$	−31.5000	−	18.1865i	−1.14187	−	0.659261i	−0.194980	−	0.980807i	$-0.562464\pi$
$761$	−31.5000	−	18.1865i	−1.14187	−	0.659261i	−0.946894	+	0.321546i	$0.895798\pi$
$762$			3.46410i			0.125491i
$763$	12.0000	−	20.7846i	0.434429	−	0.752453i
$764$	−3.00000	−	5.19615i	−0.108536	−	0.187990i
$765$	6.00000	−	3.46410i	0.216930	−	0.125245i
$766$	24.0000			0.867155
$767$	−12.0000	+	48.4974i	−0.433295	+	1.75114i
$768$	−19.0000			−0.685603
$769$	−30.0000	+	17.3205i	−1.08183	+	0.624593i	−0.931389	−	0.364026i	$-0.881402\pi$
$769$	−30.0000	+	17.3205i	−1.08183	+	0.624593i	−0.150439	+	0.988619i	$0.548069\pi$
$770$	−18.0000	−	31.1769i	−0.648675	−	1.12354i
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$			13.8564i			0.498703i
$773$	30.0000	+	17.3205i	1.07903	+	0.622975i	0.930633	−	0.365953i	$-0.119257\pi$
$773$	30.0000	+	17.3205i	1.07903	+	0.622975i	0.148392	+	0.988929i	$0.452590\pi$
$774$	24.0000	+	13.8564i	0.862662	+	0.498058i
$775$			12.1244i			0.435520i
$776$	6.00000	−	10.3923i	0.215387	−	0.373062i
$777$	−6.00000	−	10.3923i	−0.215249	−	0.372822i
$778$	−22.5000	+	12.9904i	−0.806664	+	0.465728i
$779$	48.0000			1.71978
$780$	12.0000	−	3.46410i	0.429669	−	0.124035i
$781$	12.0000			0.429394
$782$	−4.50000	+	2.59808i	−0.160920	+	0.0929070i
$783$	15.0000	+	25.9808i	0.536056	+	0.928477i
$784$	10.0000	−	17.3205i	0.357143	−	0.618590i
$785$			17.3205i			0.618195i
$786$	18.0000	+	10.3923i	0.642039	+	0.370681i
$787$	−22.5000	−	12.9904i	−0.802038	−	0.463057i	0.0421450	−	0.999112i	$-0.486581\pi$
$787$	−22.5000	−	12.9904i	−0.802038	−	0.463057i	−0.844183	+	0.536054i	$0.819914\pi$
$788$		0			0
$789$	6.00000	−	10.3923i	0.213606	−	0.369976i
$790$	3.00000	+	5.19615i	0.106735	+	0.184871i
$791$	−9.00000	+	5.19615i	−0.320003	+	0.184754i
$792$	12.0000			0.426401
$793$	14.0000	+	3.46410i	0.497155	+	0.123014i
$794$	−42.0000			−1.49052
$795$	−27.0000	+	15.5885i	−0.957591	+	0.552866i
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	−4.50000	+	7.79423i	−0.159398	+	0.276086i	−0.934652	−	0.355564i	$-0.884289\pi$
$797$	−4.50000	+	7.79423i	−0.159398	+	0.276086i	0.775254	+	0.631650i	$0.217622\pi$
$798$			20.7846i			0.735767i
$799$	3.00000	+	1.73205i	0.106132	+	0.0612756i
$800$	−31.5000	−	18.1865i	−1.11369	−	0.642991i
$801$			31.1769i			1.10158i
$802$	21.0000	−	36.3731i	0.741536	−	1.28438i
$803$	24.0000	+	41.5692i	0.846942	+	1.46695i
$804$		0			0
$805$	−18.0000			−0.634417
$806$	−7.50000	+	7.79423i	−0.264176	+	0.274540i
$807$	−24.0000			−0.844840
$808$	9.00000	−	5.19615i	0.316619	−	0.182800i
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$	3.00000	−	5.19615i	0.105409	−	0.182574i
$811$		−	46.7654i		−	1.64215i	−0.570817	−	0.821077i	$-0.693374\pi$
$811$		−	46.7654i		−	1.64215i	0.570817	−	0.821077i	$-0.306626\pi$
$812$	−9.00000	−	5.19615i	−0.315838	−	0.182349i
$813$	−15.0000	−	8.66025i	−0.526073	−	0.303728i
$814$		−	41.5692i		−	1.45700i
$815$	18.0000	−	31.1769i	0.630512	−	1.09208i
$816$	2.50000	+	4.33013i	0.0875175	+	0.151585i
$817$	48.0000	−	27.7128i	1.67931	−	0.969549i
$818$	−51.0000			−1.78317
$819$	9.00000	+	8.66025i	0.314485	+	0.302614i
$820$	−24.0000			−0.838116
$821$	30.0000	−	17.3205i	1.04701	−	0.604490i	0.125197	−	0.992132i	$-0.460044\pi$
$821$	30.0000	−	17.3205i	1.04701	−	0.604490i	0.921810	+	0.387642i	$0.126710\pi$
$822$	19.5000	+	33.7750i	0.680141	+	1.17804i
$823$	−20.5000	+	35.5070i	−0.714585	+	1.23770i	0.248534	+	0.968623i	$0.420051\pi$
$823$	−20.5000	+	35.5070i	−0.714585	+	1.23770i	−0.963119	+	0.269075i	$0.913282\pi$
$824$			24.2487i			0.844744i
$825$	−21.0000	−	12.1244i	−0.731126	−	0.422116i
$826$	36.0000	+	20.7846i	1.25260	+	0.723189i
$827$			36.3731i			1.26482i	0.774636	+	0.632408i	$0.217933\pi$
$827$			36.3731i			1.26482i	−0.774636	+	0.632408i	$0.782067\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	0.980642	+	0.195810i	$0.0627335\pi$
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	−0.320745	+	0.947166i	$0.603933\pi$
$830$	54.0000	−	31.1769i	1.87437	−	1.08217i
$831$	−26.0000			−0.901930
$832$	1.00000	+	3.46410i	0.0346688	+	0.120096i
$833$	−4.00000			−0.138592
$834$	19.5000	−	11.2583i	0.675230	−	0.389844i
$835$	−15.0000	−	25.9808i	−0.519096	−	0.899101i
$836$	−12.0000	+	20.7846i	−0.415029	+	0.718851i
$837$		−	8.66025i		−	0.299342i
$838$	31.5000	+	18.1865i	1.08815	+	0.628243i
$839$	−22.5000	−	12.9904i	−0.776786	−	0.448478i	0.0585039	−	0.998287i	$-0.481367\pi$
$839$	−22.5000	−	12.9904i	−0.776786	−	0.448478i	−0.835290	+	0.549809i	$0.814700\pi$
$840$			10.3923i			0.358569i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−10.5000	−	18.1865i	−0.361854	−	0.626749i
$843$	−1.50000	+	0.866025i	−0.0516627	+	0.0298275i
$844$	−13.0000			−0.447478
$845$	−24.0000	−	38.1051i	−0.825625	−	1.31086i
$846$	12.0000			0.412568
$847$	−1.50000	+	0.866025i	−0.0515406	+	0.0297570i
$848$	22.5000	+	38.9711i	0.772653	+	1.33827i
$849$	0.500000	−	0.866025i	0.0171600	−	0.0297219i
$850$			12.1244i			0.415862i
$851$	−18.0000	−	10.3923i	−0.617032	−	0.356244i
$852$	3.00000	+	1.73205i	0.102778	+	0.0593391i
$853$		−	17.3205i		−	0.593043i	−0.955026	−	0.296521i	$-0.904173\pi$
$853$		−	17.3205i		−	0.593043i	0.955026	−	0.296521i	$-0.0958266\pi$
$854$	6.00000	−	10.3923i	0.205316	−	0.355617i
$855$	−24.0000	−	41.5692i	−0.820783	−	1.42164i
$856$	18.0000	−	10.3923i	0.615227	−	0.355202i
$857$	24.0000			0.819824			0.409912	−	0.912125i	$-0.365559\pi$
$857$	24.0000			0.819824			0.409912	+	0.912125i	$0.365559\pi$
$858$	−6.00000	−	20.7846i	−0.204837	−	0.709575i
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	−24.0000	+	13.8564i	−0.818393	+	0.472500i
$861$	6.00000	+	10.3923i	0.204479	+	0.354169i
$862$	−16.5000	+	28.5788i	−0.561992	+	0.973399i
$863$		−	6.92820i		−	0.235839i	−0.993023	−	0.117919i	$-0.962378\pi$
$863$		−	6.92820i		−	0.235839i	0.993023	−	0.117919i	$-0.0376224\pi$
$864$	22.5000	+	12.9904i	0.765466	+	0.441942i
$865$	18.0000	+	10.3923i	0.612018	+	0.353349i
$866$		−	50.2295i		−	1.70687i
$867$	0.500000	−	0.866025i	0.0169809	−	0.0294118i
$868$	1.50000	+	2.59808i	0.0509133	+	0.0881845i
$869$	3.00000	−	1.73205i	0.101768	−	0.0587558i
$870$	−36.0000			−1.22051
$871$		0			0
$872$	−24.0000			−0.812743
$873$	−12.0000	+	6.92820i	−0.406138	+	0.234484i
$874$	18.0000	+	31.1769i	0.608859	+	1.05457i
$875$	−6.00000	+	10.3923i	−0.202837	+	0.351324i
$876$			13.8564i			0.468165i
$877$	−48.0000	−	27.7128i	−1.62084	−	0.935795i	−0.986694	−	0.162585i	$-0.948017\pi$
$877$	−48.0000	−	27.7128i	−1.62084	−	0.935795i	−0.634150	−	0.773210i	$-0.718650\pi$
$878$	−12.0000	−	6.92820i	−0.404980	−	0.233816i
$879$			15.5885i			0.525786i
$880$	−30.0000	+	51.9615i	−1.01130	+	1.75162i
$881$	−6.00000	−	10.3923i	−0.202145	−	0.350126i	0.747074	−	0.664741i	$-0.231458\pi$
$881$	−6.00000	−	10.3923i	−0.202145	−	0.350126i	−0.949219	+	0.314615i	$0.898125\pi$
$882$	−12.0000	+	6.92820i	−0.404061	+	0.233285i
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$	−2.50000	+	2.59808i	−0.0840841	+	0.0873828i
$885$	48.0000			1.61350
$886$	−36.0000	+	20.7846i	−1.20944	+	0.698273i
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$	−6.00000	+	10.3923i	−0.201347	+	0.348743i
$889$		−	3.46410i		−	0.116182i
$890$	−81.0000	−	46.7654i	−2.71513	−	1.56758i
$891$	−3.00000	−	1.73205i	−0.100504	−	0.0580259i
$892$		0			0
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$		0			0
$895$	−18.0000	+	10.3923i	−0.601674	+	0.347376i
$896$	21.0000			0.701561
$897$	−10.5000	−	2.59808i	−0.350585	−	0.0867472i
$898$	−30.0000			−1.00111
$899$	9.00000	−	5.19615i	0.300167	−	0.173301i
$900$	7.00000	+	12.1244i	0.233333	+	0.404145i
$901$	4.50000	−	7.79423i	0.149917	−	0.259663i
$902$			41.5692i			1.38410i
$903$	12.0000	+	6.92820i	0.399335	+	0.230556i
$904$	9.00000	+	5.19615i	0.299336	+	0.172821i
$905$			27.7128i			0.921205i
$906$	−6.00000	+	10.3923i	−0.199337	+	0.345261i
$907$	−3.50000	−	6.06218i	−0.116216	−	0.201291i	0.802049	−	0.597258i	$-0.203743\pi$
$907$	−3.50000	−	6.06218i	−0.116216	−	0.201291i	−0.918265	+	0.395966i	$0.870410\pi$
$908$	7.50000	−	4.33013i	0.248896	−	0.143700i
$909$	−12.0000			−0.398015
$910$	−36.0000	+	10.3923i	−1.19339	+	0.344502i
$911$	−9.00000			−0.298183			−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000			−0.298183			−0.149092	+	0.988823i	$0.547635\pi$
$912$	30.0000	−	17.3205i	0.993399	−	0.573539i
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$	10.5000	−	18.1865i	0.347309	−	0.601557i
$915$		−	13.8564i		−	0.458079i
$916$	−13.5000	−	7.79423i	−0.446053	−	0.257529i
$917$	−18.0000	−	10.3923i	−0.594412	−	0.343184i
$918$		−	8.66025i		−	0.285831i
$919$	−29.0000	+	50.2295i	−0.956622	+	1.65692i	−0.226009	+	0.974125i	$0.572568\pi$
$919$	−29.0000	+	50.2295i	−0.956622	+	1.65692i	−0.730613	+	0.682792i	$0.760765\pi$
$920$	9.00000	+	15.5885i	0.296721	+	0.513936i
$921$	3.00000	−	1.73205i	0.0988534	−	0.0570730i
$922$	−33.0000			−1.08680
$923$	3.00000	−	12.1244i	0.0987462	−	0.399078i
$924$	−6.00000			−0.197386
$925$	−42.0000	+	24.2487i	−1.38095	+	0.797293i
$926$	−33.0000	−	57.1577i	−1.08445	−	1.87832i
$927$	14.0000	−	24.2487i	0.459820	−	0.796432i
$928$			31.1769i			1.02343i
$929$	39.0000	+	22.5167i	1.27955	+	0.738748i	0.976765	−	0.214312i	$-0.0687509\pi$
$929$	39.0000	+	22.5167i	1.27955	+	0.738748i	0.302783	+	0.953059i	$0.402084\pi$
$930$	9.00000	+	5.19615i	0.295122	+	0.170389i
$931$			27.7128i			0.908251i
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	6.00000	+	10.3923i	0.196431	+	0.340229i
$934$	45.0000	−	25.9808i	1.47244	−	0.850117i
$935$	12.0000			0.392442
$936$	3.00000	−	12.1244i	0.0980581	−	0.396297i
$937$	−35.0000			−1.14340			−0.571700	−	0.820463i	$-0.693716\pi$
$937$	−35.0000			−1.14340			−0.571700	+	0.820463i	$0.693716\pi$
$938$		0			0
$939$	5.00000	+	8.66025i	0.163169	+	0.282617i
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$		−	3.46410i		−	0.112926i	−0.998405	−	0.0564632i	$-0.982018\pi$
$941$		−	3.46410i		−	0.112926i	0.998405	−	0.0564632i	$-0.0179824\pi$
$942$	7.50000	+	4.33013i	0.244363	+	0.141083i
$943$	18.0000	+	10.3923i	0.586161	+	0.338420i
$944$		−	69.2820i		−	2.25494i
$945$	15.0000	−	25.9808i	0.487950	−	0.845154i
$946$	24.0000	+	41.5692i	0.780307	+	1.35153i
$947$	10.5000	−	6.06218i	0.341204	−	0.196994i	−0.319600	−	0.947552i	$-0.603549\pi$
$947$	10.5000	−	6.06218i	0.341204	−	0.196994i	0.660804	+	0.750558i	$0.270215\pi$
$948$	1.00000			0.0324785
$949$	48.0000	−	13.8564i	1.55815	−	0.449798i
$950$	84.0000			2.72532
$951$	−9.00000	+	5.19615i	−0.291845	+	0.168497i
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	19.5000	−	33.7750i	0.631667	−	1.09408i	−0.355544	−	0.934660i	$-0.615704\pi$
$953$	19.5000	−	33.7750i	0.631667	−	1.09408i	0.987211	−	0.159420i	$-0.0509623\pi$
$954$		−	31.1769i		−	1.00939i
$955$	18.0000	+	10.3923i	0.582466	+	0.336287i
$956$	−21.0000	−	12.1244i	−0.679189	−	0.392130i
$957$			20.7846i			0.671871i
$958$	−31.5000	+	54.5596i	−1.01772	+	1.76274i
$959$	−19.5000	−	33.7750i	−0.629688	−	1.09065i
$960$	3.00000	−	1.73205i	0.0968246	−	0.0559017i
$961$	28.0000			0.903226
$962$	−42.0000	−	10.3923i	−1.35413	−	0.335061i
$963$	−24.0000			−0.773389
$964$	12.0000	−	6.92820i	0.386494	−	0.223142i
$965$	−24.0000	−	41.5692i	−0.772587	−	1.33816i
$966$	−4.50000	+	7.79423i	−0.144785	+	0.250775i
$967$			3.46410i			0.111398i	0.998448	+	0.0556990i	$0.0177387\pi$
$967$			3.46410i			0.111398i	−0.998448	+	0.0556990i	$0.982261\pi$
$968$	1.50000	+	0.866025i	0.0482118	+	0.0278351i
$969$	−6.00000	−	3.46410i	−0.192748	−	0.111283i
$970$		−	41.5692i		−	1.33471i
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	−0.910140	−	0.414301i	$-0.864026\pi$
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	0.813865	+	0.581054i	$0.197359\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$	−19.5000	+	11.2583i	−0.625141	+	0.360925i
$974$	9.00000			0.288379
$975$	−17.5000	+	18.1865i	−0.560449	+	0.582435i
$976$	−20.0000			−0.640184
$977$	12.0000	−	6.92820i	0.383914	−	0.221653i	−0.295606	−	0.955310i	$-0.595521\pi$
$977$	12.0000	−	6.92820i	0.383914	−	0.221653i	0.679520	+	0.733657i	$0.262188\pi$
$978$	−9.00000	−	15.5885i	−0.287788	−	0.498464i
$979$	−27.0000	+	46.7654i	−0.862924	+	1.49463i
$980$		−	13.8564i		−	0.442627i
$981$	24.0000	+	13.8564i	0.766261	+	0.442401i
$982$	−45.0000	−	25.9808i	−1.43601	−	0.829079i
$983$			22.5167i			0.718170i	0.933305	+	0.359085i	$0.116911\pi$
$983$			22.5167i			0.718170i	−0.933305	+	0.359085i	$0.883089\pi$
$984$	6.00000	−	10.3923i	0.191273	−	0.331295i
$985$		0			0
$986$	9.00000	−	5.19615i	0.286618	−	0.165479i
$987$	6.00000			0.190982
$988$	18.0000	+	17.3205i	0.572656	+	0.551039i
$989$	24.0000			0.763156
$990$	36.0000	−	20.7846i	1.14416	−	0.660578i
$991$	12.5000	+	21.6506i	0.397076	+	0.687755i	0.993364	−	0.115015i	$-0.0366917\pi$
$991$	12.5000	+	21.6506i	0.397076	+	0.687755i	−0.596288	+	0.802771i	$0.703358\pi$
$992$	4.50000	−	7.79423i	0.142875	−	0.247467i
$993$		−	10.3923i		−	0.329790i
$994$	−9.00000	−	5.19615i	−0.285463	−	0.164812i
$995$	−48.0000	−	27.7128i	−1.52170	−	0.878555i
$996$		−	10.3923i		−	0.329293i
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	−0.554554	−	0.832148i	$-0.687111\pi$
$997$	14.0000	−	24.2487i	0.443384	−	0.767964i	0.997938	+	0.0641836i	$0.0204443\pi$
$998$	25.5000	+	44.1673i	0.807188	+	1.39809i
$999$	30.0000	−	17.3205i	0.949158	−	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	221.2.m.a.205.1	yes	2
13.2	odd	12		2873.2.a.e.1.2		2
13.4	even	6	inner	221.2.m.a.69.1	✓	2
13.11	odd	12		2873.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.m.a.69.1	✓	2	13.4	even	6	inner
221.2.m.a.205.1	yes	2	1.1	even	1	trivial
2873.2.a.e.1.1		2	13.11	odd	12
2873.2.a.e.1.2		2	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 221 = 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	221.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(1.50000 + 0.866025i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(3.00000 + 5.19615i) q^{10} +(3.00000 - 1.73205i) q^{11} +1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} -3.00000 q^{14} +(-3.00000 + 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(0.500000 - 0.866025i) q^{17} -3.46410i q^{18} +(-6.00000 - 3.46410i) q^{19} +(3.00000 + 1.73205i) q^{20} -1.73205i q^{21} +(3.00000 - 5.19615i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(-1.50000 + 0.866025i) q^{24} -7.00000 q^{25} +(-4.50000 - 4.33013i) q^{26} +5.00000 q^{27} +(-1.50000 + 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} +(-3.00000 + 5.19615i) q^{30} -1.73205i q^{31} +(4.50000 + 2.59808i) q^{32} +(3.00000 + 1.73205i) q^{33} -1.73205i q^{34} +(3.00000 - 5.19615i) q^{35} +(-1.00000 - 1.73205i) q^{36} +(6.00000 - 3.46410i) q^{37} -12.0000 q^{38} +(2.50000 - 2.59808i) q^{39} -6.00000 q^{40} +(-6.00000 + 3.46410i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(-4.00000 + 6.92820i) q^{43} -3.46410i q^{44} +(6.00000 + 3.46410i) q^{45} +(-4.50000 - 2.59808i) q^{46} +3.46410i q^{47} +(-2.50000 + 4.33013i) q^{48} +(-2.00000 - 3.46410i) q^{49} +(-10.5000 + 6.06218i) q^{50} +1.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} +9.00000 q^{53} +(7.50000 - 4.33013i) q^{54} +(6.00000 + 10.3923i) q^{55} +(1.50000 - 2.59808i) q^{56} -6.92820i q^{57} +(9.00000 + 5.19615i) q^{58} +(-12.0000 - 6.92820i) q^{59} +3.46410i q^{60} +(-2.00000 + 3.46410i) q^{61} +(-1.50000 - 2.59808i) q^{62} +(-3.00000 + 1.73205i) q^{63} -1.00000 q^{64} +(12.0000 - 3.46410i) q^{65} +6.00000 q^{66} +(-0.500000 - 0.866025i) q^{68} +(1.50000 - 2.59808i) q^{69} -10.3923i q^{70} +(3.00000 + 1.73205i) q^{71} +(3.00000 + 1.73205i) q^{72} +13.8564i q^{73} +(6.00000 - 10.3923i) q^{74} +(-3.50000 - 6.06218i) q^{75} +(-6.00000 + 3.46410i) q^{76} -6.00000 q^{77} +(1.50000 - 6.06218i) q^{78} +1.00000 q^{79} +(-15.0000 + 8.66025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} -10.3923i q^{83} +(-1.50000 - 0.866025i) q^{84} +(3.00000 + 1.73205i) q^{85} +13.8564i q^{86} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-13.5000 + 7.79423i) q^{89} +12.0000 q^{90} +(-1.50000 + 6.06218i) q^{91} -3.00000 q^{92} +(1.50000 - 0.866025i) q^{93} +(3.00000 + 5.19615i) q^{94} +(12.0000 - 20.7846i) q^{95} +5.19615i q^{96} +(-6.00000 - 3.46410i) q^{97} +(-6.00000 - 3.46410i) q^{98} -6.92820i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} - 3 q^{7} + 2 q^{9} + 6 q^{10} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 6 q^{14} - 6 q^{15} + 5 q^{16} + q^{17} - 12 q^{19} + 6 q^{20} + 6 q^{22} - 3 q^{23} - 3 q^{24}+ \cdots - 12 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 + q^3 + q^4 + 3 * q^6 - 3 * q^7 + 2 * q^9 + 6 * q^10 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 6 * q^14 - 6 * q^15 + 5 * q^16 + q^17 - 12 * q^19 + 6 * q^20 + 6 * q^22 - 3 * q^23 - 3 * q^24 - 14 * q^25 - 9 * q^26 + 10 * q^27 - 3 * q^28 + 6 * q^29 - 6 * q^30 + 9 * q^32 + 6 * q^33 + 6 * q^35 - 2 * q^36 + 12 * q^37 - 24 * q^38 + 5 * q^39 - 12 * q^40 - 12 * q^41 - 3 * q^42 - 8 * q^43 + 12 * q^45 - 9 * q^46 - 5 * q^48 - 4 * q^49 - 21 * q^50 + 2 * q^51 - 7 * q^52 + 18 * q^53 + 15 * q^54 + 12 * q^55 + 3 * q^56 + 18 * q^58 - 24 * q^59 - 4 * q^61 - 3 * q^62 - 6 * q^63 - 2 * q^64 + 24 * q^65 + 12 * q^66 - q^68 + 3 * q^69 + 6 * q^71 + 6 * q^72 + 12 * q^74 - 7 * q^75 - 12 * q^76 - 12 * q^77 + 3 * q^78 + 2 * q^79 - 30 * q^80 - q^81 - 12 * q^82 - 3 * q^84 + 6 * q^85 - 6 * q^87 + 6 * q^88 - 27 * q^89 + 24 * q^90 - 3 * q^91 - 6 * q^92 + 3 * q^93 + 6 * q^94 + 24 * q^95 - 12 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more